# Scalene Triangle

Before talking about the properties of the scalene triangle,  let us know what a triangle is?. And also learn about the different types of a triangle based on its sides and angles.

## Triangle Definition

In geometry, a triangle is a closed two-dimensional plane figure with three sides and three angles. A triangle is considered as a three-sided polygon.

Based on the sides and the interior angles of a triangle, a triangle can be classified into different types. According to the interior angles of the triangle, it can be classified as three types, namely

Acute Angle Triangle: A triangle which consists of three acute angles in which all the angles are less than 90 degrees

Right Angle Triangle: A triangle in which one angle measures 90 degrees and other two angles are less than 90 degrees(acute angles)

Obtuse Angle Triangle: A triangle in which one angle measures above 90 degrees and the other two angles that measure less than 90 degrees.

According to the sides of the triangle, the triangle can be classified into three types, namely

Scalene Triangle: A triangle with no equal sides or a triangle in which all the sides of a triangle are of different length.

Isosceles Triangle: A triangle with two equal sides and two equal angles is called an isosceles triangle. Also, two angles of the triangle are of the same measure

Equilateral Triangle: A triangle in which all three sides are equal and each interior angles of a triangle measure 60 degrees is called the equilateral triangle

Here we will discuss a few properties of a scalene triangle in detail.

## Scalene Triangle Definition

A scalene triangle is a triangle in which all the sides of a triangle are of different length and all the angles of a triangle are of different measures where the sum of the interior three angles of a triangle is always equal to 180 degrees.

## Scalene Triangle Formulas

The formulas to find the area and perimeter of a scalene triangle is given and explained below.

### Area of a Scalene Triangle

The area of scalene triangle = (1/2) x b x h square units

Where,

“b” refers to the base of the triangle

“h” refers to the height of a triangle

If the sides of the triangle are given, then apply the Heron’s formula

The area of the scalene triangle =  $A = \sqrt{S (S-a)(S-b)(S-c)}$ square units

Where S is the semiperimeter of a triangle

It can be found using the formula

S = (a+b+c)/2

Here,

a, b, and c denotes the sides of the triangle

### The perimeter of a Scalene Triangle

The perimeter of a scalene triangle is equal to the sum of the length of sides of a triangle and it is given as

Perimeter of a scalene triangle = a + b + c units

Consider a given triangle

To find the perimeter for the given triangle, then add the sides of a triangle

Therefore, perimeter = 15 + 34 + 32 = 81 cm

### Scalene Triangle Properties

Some of the important properties of the scalene triangle are as follows:

• A scalene triangle has no equal sides
• It has no equal angles
• It has no line symmetry
• It has no point symmetry.
• The angles inside the scalene triangle can be an acute, obtuse or right angle.
• If all the angles of the triangle are less than 90 degrees(acute), then the centre of the circumscribing circle will lie inside a triangle.
• In a scalene obtuse triangle, the circumcenter will lie outside the triangle.

### Sample Problem

The sample example for the scalene triangle is given below.

Question:

Find the area of the scalene triangle ABC with the sides 8cm, 6cm and 4cm

Solution:

Let a= 8 cm

b = 6 cm

c = 4 cm

If all the sides of a triangle are given, then use Heron’s formula

The area of the scalene triangle =  $\sqrt{S (S-a)(S-b)(S-c)}$

Now, find the semiperimeter value

S = (a+b+c)/2

S = (8+6+4)/2

S = 18/2

S = 9

Now substitute the value of S in the area formula,

Area = $\sqrt{9(9-8)(9-6)(9-4)}$

$=\sqrt{9(1)(3)(5)}$

$=\sqrt{135}$

=11.6

Therefore, the area of the scalene triangle = 11.6 square units.

For more such interesting information on properties of a scalene triangle, and some other quadrilateral properties, register with BYJU’S – The Learning App and also watch videos to learn with ease.

#### Practise This Question

If the sides of a triangle are 39 cm, 80 cm, and 89 cm, then the triangle formed is a _____ triangle.